Volume Concepts

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Answer Key & Explanations

Volume Concepts · Grade 5 · Worksheet 1

1. Emma is designing a fish tank for her classroom. The tank is shaped like a rectangular prism and measures 1.2 meters in length, 0.75 meters in width, and 0.9 meters in height. If she fills the tank completely with water, what is the volume of water in cubic meters? Answer: 0.81 Solution: Identify the dimensions: length = 1.2 m, width = 0.75 m, height = 0.9 m Use the volume formula for a rectangular prism: Volume = length × width × height Multiply the numbers: 1.2 × 0.75 = 0.9 Multiply the result by the height: 0.9 × 0.9 = 0.81 The volume is 0.81 cubic meters
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 1.2 m, width = 0.75 m, height = 0.9 m Step 2: Use the volume formula for a rectangular prism: Volume = length × width × height Step 3: Multiply the numbers: 1.2 × 0.75 = 0.9 Step 4: Multiply the result by the height: 0.9 × 0.9 = 0.81 Step 5: The volume is 0.81 cubic meters

2. Charlotte is helping her family move into a new house. She has a rectangular storage bin that measures 12 inches long, 10 inches wide, and 8 inches tall. She wants to fill the bin completely with packing cubes that are each 1 cubic inch. How many packing cubes can Charlotte fit in the storage bin? Answer: 960 Solution: The storage bin is a rectangular prism. Volume is the number of unit cubes that fit inside. Since each packing cube is 1 cubic inch, the volume in cubic inches equals the number of cubes.
   Full step-by-step solution

   Step 1: The storage bin is a rectangular prism. Volume is the number of unit cubes that fit inside. Since each packing cube is 1 cubic inch, the volume in cubic inches equals the number of cubes. Step 2: Use the formula for volume of a rectangular prism: Volume = length x width x height. Step 3: Plug in the dimensions: Volume = 12 x 10 x 8. Step 4: Multiply length and width: 12 x 10 = 120. Step 5: Multiply by the height: 120 x 8 = 960. Step 6: The volume is 960 cubic inches, so Charlotte can fit 960 packing cubes. The answer is 960.

3. A shipping company needs to pack a large rectangular crate that measures 2.4 meters long, 1.5 meters wide, and 1.2 meters high. What is the volume of the crate in cubic meters? Answer: 4.32 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given measurements: Volume = 2.4 × 1.5 × 1.2 First multiply 2.4 × 1.5 = 3.6 Then multiply 3.6 × 1.2 = 4.32 The volume is 4.32 cubic meters The answer is 4.32.
   Full step-by-step solution

   Step 1: Identify the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given measurements: Volume = 2.4 × 1.5 × 1.2 Step 3: First multiply 2.4 × 1.5 = 3.6 Step 4: Then multiply 3.6 × 1.2 = 4.32 Step 5: The volume is 4.32 cubic meters The answer is 4.32.

4. (24 × 15 × 8) ÷ 12 = ? Answer: 240 Solution: Multiply 24 × 15 24 × 15 = 360 Multiply the result by 8 360 × 8 = 2880 Divide by 12 2880 ÷ 12 = 240 The answer is 240.
   Full step-by-step solution

   Step 1: Multiply 24 × 15 24 × 15 = 360 Step 2: Multiply the result by 8 360 × 8 = 2880 Step 3: Divide by 12 2880 ÷ 12 = 240 The answer is 240.

5. (25 × 16 × 12) ÷ 8 = ? Answer: 600 Solution: Multiply the first two dimensions: 25 × 16 = 400 Multiply the result by the third dimension: 400 × 12 = 4800 Divide the total by 8: 4800 ÷ 8 = 600 The answer is 600.
   Full step-by-step solution

   Step 1: Multiply the first two dimensions: 25 × 16 = 400 Step 2: Multiply the result by the third dimension: 400 × 12 = 4800 Step 3: Divide the total by 8: 4800 ÷ 8 = 600 The answer is 600.

6. (32 × 25 × 18) ÷ 12 = ? Answer: 1200 Solution: Multiply the first two dimensions: 32 × 25 = 800 Multiply the result by the third dimension: 800 × 18 = 14400 Divide the total by 12: 14400 ÷ 12 = 1200 The answer is 1200.
   Full step-by-step solution

   Step 1: Multiply the first two dimensions: 32 × 25 = 800 Step 2: Multiply the result by the third dimension: 800 × 18 = 14400 Step 3: Divide the total by 12: 14400 ÷ 12 = 1200 The answer is 1200.

7. A shipping company is packing books into rectangular boxes. Each box measures 2.4 meters long, 1.5 meters wide, and 0.8 meters high. If they completely fill one box with books, what is the volume of books in cubic meters? Answer: 2.88 Solution: Identify the dimensions: length = 2.4 m, width = 1.5 m, height = 0.8 m Use the volume formula for a rectangular prism: Volume = length × width × height Multiply the dimensions: 2.4 × 1.5 = 3.6 Multiply the result by the height: 3.6 × 0.8 = 2.88 The volume is 2.88 cubic meters.
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 2.4 m, width = 1.5 m, height = 0.8 m Step 2: Use the volume formula for a rectangular prism: Volume = length × width × height Step 3: Multiply the dimensions: 2.4 × 1.5 = 3.6 Step 4: Multiply the result by the height: 3.6 × 0.8 = 2.88 Step 5: The volume is 2.88 cubic meters.

8. ∛1331 = ? Answer: 11 Solution: We need to find the cube root of 1331, which means finding a number that when multiplied by itself three times equals 1331.
   Full step-by-step solution

   Step 1: We need to find the cube root of 1331, which means finding a number that when multiplied by itself three times equals 1331. Step 2: Try 10: 10 × 10 × 10 = 1000 (too small) Step 3: Try 11: 11 × 11 × 11 = 121 × 11 = 1331 Step 4: Since 11 × 11 × 11 = 1331, the cube root of 1331 is 11. The answer is 11.

9. ∛2197 = ? Answer: 13 Solution: We need to find the cube root of 2197, which means finding a number that when multiplied by itself three times equals 2197.
   Full step-by-step solution

   Step 1: We need to find the cube root of 2197, which means finding a number that when multiplied by itself three times equals 2197. Step 2: Try 10: 10 × 10 × 10 = 1000 (too small) Step 3: Try 12: 12 × 12 × 12 = 144 × 12 = 1728 (still too small) Step 4: Try 13: 13 × 13 × 13 = 169 × 13 = 2197 Step 5: Since 13 × 13 × 13 = 2197, the cube root of 2197 is 13. The answer is 13.